# Including off-diagonal anisotropies in anisotropic hydrodynamics

## TL;DR

This paper introduces an efficient method to incorporate off-diagonal local rest frame momentum anisotropies into anisotropic hydrodynamics by diagonalizing the anisotropy tensor, simplifying calculations of relevant moments.

## Contribution

The authors develop a novel diagonalization-based approach to include off-diagonal anisotropies in leading-order anisotropic hydrodynamics, reducing computational complexity.

## Key findings

- Method efficiently includes off-diagonal anisotropies.
- Framework applicable to energy-momentum tensor calculations.
- Simplifies viscous update equations in anisotropic hydrodynamics.

## Abstract

In this paper we present a method for efficiently including the effects of off-diagonal local rest frame momentum anisotropies in leading-order anisotropic hydrodynamics. The method relies on diagonalization of the space-like block of the anisotropy tensor and allows one to reduce the necessary moments of the distribution function in the off-diagonal case to a linear combination of diagonal-anisotropy integrals. Once reduced to diagonal-anisotropy integrals, the results can be computed efficiently using techniques described previously in the literature. We present a general framework for how to accomplish this and provide examples for off-diagonal anisotropy moments entering into the energy-momentum tensor and viscous update equations which emerge when performing anisotropic pressure matching.